Back in 2004 I was charged with a domestic battery, it has been 10 years and have not been into any trouble, I would like to start a career but I would like to know before I pay the money to challeng the test

I would like to say go ahead, but any offence on your record, no matter when, would still show up in a background check. You have this under healthcare, any application would require a background check and the healthcare field would not allow a felon in any form.

They run specific backgrounds for domestic violence at the last three health care companies I worked for Any conviction, they would not hire

You did not say if it was a felony or not, if a felony, no, you can no for sure

http://definitions.uslegal.com/w/withheld-adjudication/
If you are in the US, call your state licensing board medical division. Tell them the specifics and the disposition as stated on your paperwork.
They aren't going to get your name and put you in a file, so ask all the questions you want.
I think you have a pretty good chance of being able to belicensed based on what you say.
I would also go in person to the courthouse records to see exactly what is there about you! It's possible that it won't be on a background check.